Peter isn't calling these people dogs. He's simply using this proverb to illustrate what their behavior is like.
"For if, after they have escaped the pollutions of the world through the knowledge of the Lord and Savior Jesus Christ, they are again entangled in them and overcome, the latter end is worse for them than the beginning. For it would have been better for them not to have known the way of righteousness, than having known it, to turn from the holy commandment delivered to them. But it has happened to them according to the true proverb: 'A dog returns to his own vomit,' and, 'a sow, having washed, to her wallowing in the mire.' " 2 Peter 2:20-22
This is so elementary and so obvious I can hardly believe it needs explaining.